In Figure REF  we show the high-weight network \(R_n(I_0)\)  with a maximum flow. There is one minimum cut, \(c_T = \lbrace (s,\rho _0),(\rho _4,t)\rbrace \) . Note that \(c_T\)  is a cut since removing these edges leaves no path from \(s\)  to \(t\) . By the Max Flow-Min Cut Theorem [1]}, it is also a minimum cut since the capacity of \(c_T\)  (1157100512) is equal to the value of a maximum flow.
For this cut \(c_T\)  we list every rotation \(\rho \)  such that \((\rho ,t)\)  is an edge in \(R_n(I)\)  and \((\rho ,t)\notin c_T\) . Then a maximum weight closed subset of the rotation poset is given by this set of rotations and their predecessors. \(c_T\)  has associated closed subset of \(\lbrace \rho _0,\rho _1,\rho _2\rbrace \)  which is precisely a maximum weight closed subset of \(R_p(I_0)\) . The man-optimal stable matching of \(I_0\)  is
\(M = \lbrace (m_1,w_5), (m_2,w_3), (m_3,w_8), (m_4,w_6), (m_5,w_7), (m_6,w_1), (m_7,w_2), (m_8,w_4)\rbrace .\) 
